It is critically important in many watermarking applications that the false positive probability of a watermark detector is below a given value. A false positive occurs when the watermark detector incorrectly identifies an unwatermarked work as watermarked. One example of a system where this is important is the use of a watermark in video content to indicate to a recorder or recording device that the video material should not be copied. If a false positive occurs during a recording, the recording device monitoring for that watermark will incorrectly conclude that the video content should not be copied and recording will be halted. If this occurs during the recording of a wedding ceremony, the camera manufacturer will have a very unhappy bride and groom. If this happens during a television broadcast of a popular program, the recorder manufacturers will have many unhappy customers. Thus, recorder manufacturers have typically required that such a copy control watermark have a false positive probability that is close to the probability of a hardware component failure; in the range of between 1 error in 109 detections to 1 error in 1012 detections.
To further understand the problem of false positive probability, consider the illustration shown in FIG. 2a, which shows two distributions. The distribution on the left represents the detection values that could be expected when the watermark detector is applied to content that does not contain a watermark. The mean of this distribution is zero and most often, it could be expected to be close to zero. This is a probability curve, so the area under the curve is equal to 1.0. The distribution on the right represents the detection values that could be expected when the detector is applied to watermarked content. Here, the mean is M and the detection value is usually close to M. The role of a threshold is to distinguish between samples from these two distributions. Consider the threshold at the point marked T. When the detection value exceeds T, it can be concluded that the content comes from the right-hand distribution. When the detection value is below T, it can be concluded that the content comes from the left-hand distribution. As can be seen from FIG. 2a, there are some samples from the right-hand distribution that are below the threshold T. These are marked works for which detection will fail, sometimes called false negatives. Similarly, there are some samples from the left-hand distribution that exceed the threshold. These are unmarked works that the detector will label as marked. These are false positives.
The probability of false negatives can be improved by lowering the threshold. This action will, however, simultaneously increase the probability of a false positive indication. In the example shown, the two distributions overlap. That means that a threshold that eliminates errors cannot be selected. In many watermarking applications, the detection threshold T is selected based on an application specific false positive probability requirement. It should be noted that the false positive probability is independent of the watermark embedding algorithm. It is simply the area under the left-hand curve that is greater than the threshold T.
FIG. 2b shows a closer view of the left-hand curve in the vicinity of the threshold. The area under the curve that is greater than the threshold T is shown shaded. This area represents the false positive probability, the probability that a watermark will be detected in an unmarked work.
Given a false positive probability requirement, it would be advantageous to have a method and system for establishing the lowest threshold that satisfies the false positive probability requirement.
As used herein, “/” denotes alternative names for the same or similar components or structures. That is, a “/” can be taken as meaning “or” as used herein.